Computation of Geodesies on the Ellipsoid
142
[2] Brownlee, K. A., Statistical theory and methodology in science and
engineering. New York, 1960.
[3] Chernoff, H. and L. E. Moses, Elementary decision theory. New
York, 1959.
[4] Dantzig, D. van, Statistical priesthood (Savage on personal proba
bilities). Statistica Neerlandica 11 (1957) page 1.
[5] Luce, R. D. and H. Raiffa, Games and decisions. New York, 1954.
[6] Monhemius, W., Besliskunde, een vlag die de lading dekt? Statistica
Neerlandica 17 (1963) page 329.
[7] Neumann, J. von, and O. Morgenstern, Theory of games and economie
behaviour. Princeton, 1947.
[8] Sadowski, W., The theory of decision-making. An introduction to
operations research. Warszawa, 1965.
[9] Savage, L. J., The foundations of statistics. New York, 1954.
[10] Wald, A., Statistical decision functions. New York, 1950.
Ir. J. C. P. DE KRUIF,
Computing Centre of the Delft Geodetic Institute:
1. Principles of the method
1.1 Description of the problem.
An arbitrary line on an ellipsoid can be described by four simul
taneous differential equations, a geodesic by only three.
These differential equations are of the elliptic type; they can
only be solved by methods of the numerical analysis.
One of these methods is a Taylor expansion (e.g. the formulas
of Gauss and Legendre). This method however is not so suitable
for use with a computer, because the number of derivatives of the
differential equations, that must be taken into account, depends
on the length of the line and the accuracy required. For a general
formula-system this great number of derivatives causes a compli
cated program. This method is well suited for computations
concerning lines of about the same length in a fixed area. In that
case the formulas can be simplified and the coefficients of the
formulas can be tabulated somehow.
The method to be described in this paper has been designed for
computer use and is valid for lines of any length.
1.2 Principles of the solution.
The system of simultaneous differential equations can be numeri
cally solved by the method of Runge-Kutta. This method is
directly based on the differential equations. The solution is valid
for lines of any lengththe accuracy can be influenced by varying
the step size.
